Statistical methods for time series of counts with long-range dependence arising from health care settings

卫生保健机构产生的具有长期依赖性的计数时间序列的统计方法

• 批准号: RGPIN-2017-04992
• 负责人: hussein, abdulkadir
• 金额: $ 1.46万
• 依托单位: University of Windsor
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=654143
• 关键词: Statistical; methods; time; series; counts

This proposal is an initiative to provide statistical models and inferential tools to an important type of data that arises in many fields of applications. Specifically, this proposal is intended to deal with the statistical analysis of data sets in which the outcome of interest is a long series of temporally and spatially correlated counts with a complex feature known as Long-Range Dependence (LRD) or Long-Memory behavior. ***In general, data in the form of time series of counts arise in fields of applications such as: health care performance analysis (e.g., analysis of number of patients served at the emergency department of a hospital or admitted to the hospital); monitoring of environmental pollutants; analysis of data from financial markets (e.g., counts of daily transactions for a given stock); public health surveillance (e.g., surveillance of cause-specific mortality). ******Although there is a considerable and growing attention directed to the statistical modeling and analysis of time series of counts, many of its complex aspects such as the LRD feature have not been fully addressed. The LRD feature manifests itself through the correlation structure of the data, and such behavior has been observed in some data arising from financial markets and from health care services. For instance, the number of patients at an emergence department at 8am, observed daily over several years, may sometimes exhibit an LRD behavior. In addition to the temporal LRD feature, such data may also have spatial correlations when collected at several facilities over a geographical area of interest. ******In this proposal, I intend to provide a suite of statistical modeling, inference, and surveillance tools along with software packages to implement it for spatio-temporal count data with LRD features. Specifically, I will study regression models that handle short-term (spatial and temporal) dependencies in counts through spatial and temporal ARMA(p,q) modeling approach while the temporal LRD feature is dealt with via fractional Gaussian noises (FGN) and related long-memory processes. This is an appealing approach, as often the LRD is due to a background latent process in which investigators are not interested in estimating, although statistical methods must account for it as a nuisance process. The FGNs are processes that introduce LRD by using only one parameter, known as the Hurst exponent. Thus, FGNs provide a way of handling LRD while keeping low the number of parameters to be estimated in the model. The methodologies resulting from this research project are expected to aid stakeholders in health care services, and in other areas of applications where such data arise, in making proper decisions based on the correct statistical inferences.

该提案旨在为许多应用领域中出现的重要类型的数据提供统计模型和推理工具。具体来说，该提案旨在处理数据集的统计分析，其中感兴趣的结果是一系列时间和空间相关的计数，具有称为远程依赖（LRD）或长记忆行为的复杂特征。 ***一般来说，计数时间序列形式的数据出现在以下应用领域：医疗保健绩效分析（例如，分析在医院急诊科服务或入院的患者数量）； 环境污染物监测；分析金融市场的数据（例如给定股票的每日交易计数）；公共卫生监测（例如，特定原因死亡率的监测）。 ******尽管人们越来越关注计数时间序列的统计建模和分析，但其许多复杂方面（例如 LRD 特征）尚未得到完全解决。 LRD 特征通过数据的相关结构体现出来，并且在金融市场和医疗保健服务产生的一些数据中观察到了这种行为。例如，多年来每天观察急诊科早上 8 点的患者数量，有时可能会表现出 LRD 行为。 除了时间 LRD 特征之外，当在感兴趣的地理区域的多个设施收集时，此类数据还可能具有空间相关性。 ******在本提案中，我打算提供一套统计建模、推理和监视工具以及软件包，以实现具有 LRD 功能的时空计数数据。具体来说，我将研究通过空间和时间 ARMA(p,q) 建模方法处理计数中的短期（空间和时间）依赖性的回归模型，同时通过分数高斯噪声 (FGN) 和相关的长周期处理时间 LRD 特征。 - 记忆过程。这是一种很有吸引力的方法，因为 LRD 通常是由背景潜在过程引起的，调查人员对估计不感兴趣，尽管统计方法必须将其视为一个令人讨厌的过程。 FGN 是仅使用一个参数（称为 Hurst 指数）引入 LRD 的过程。因此，FGN 提供了一种处理 LRD 的方法，同时保持模型中要估计的参数数量较少。该研究项目产生的方法预计将帮助医疗保健服务以及出现此类数据的其他应用领域的利益相关者根据正确的统计推断做出正确的决策。